Goldie ring

Let R be a ring. If the set of annihilatorsPlanetmathPlanetmathPlanetmathPlanetmath {r.ann(x)xR} satisifies the ascending chain conditionMathworldPlanetmathPlanetmathPlanetmath, then R is said to satisfy the ascending chain condition on right annihilators.

A ring R is called a right Goldie ring if it satisfies the ascending chain condition on right annihilators and RR is a module of finite rank.

Left Goldie ring is defined similarly. If the context makes it clear on which side the ring operates, then such a ring is simply called a Goldie ring.

A right Noetherian ring is right Goldie.

Title Goldie ring
Canonical name GoldieRing
Date of creation 2013-03-22 14:04:10
Last modified on 2013-03-22 14:04:10
Owner mclase (549)
Last modified by mclase (549)
Numerical id 6
Author mclase (549)
Entry type Definition
Classification msc 16P60
Synonym Goldie
Related topic UniformDimension
Defines left Goldie
Defines right Goldie
Defines left Goldie ring
Defines right Goldie ring